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Math Help - Inverse function

  1. #1
    Bud
    Bud is offline
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    Inverse function

    Hi there,

    I have some trouble understanding how to derive that the inverse function of the following function

    f(x,y) = (x+y,x-y)

    is

    f^{-1}(x,y) = \frac{1}{2}(x+y,x-y)

    So far I had no trouble in one dimension. Maybe my problem lies here somewhere...
    Thanks in advance for any help.

    Cheers
    Bud
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  2. #2
    Bud
    Bud is offline
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    Joined
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    Ok, I know what went wrong. I got confused by the notation.

    Lets rename x --> x1 and y --> x2

    from f(x1,x2) = (x1 + x2,x1 - x2) follow 2 equations:

    (I) y1 = x1 + x2 = x1 - x2 + 2*x2 ( insert in (II))
    (II) y2 = x1 - x2

    --> y2 = y1 - 2*x2
    --> x2 = 1/2*(y1 - y2) (insert in (I))

    --> y1 = x1 + 1/2(y1 - y2)
    --> x1 = 1/2*(y1 + y2)

    Thus, both x1 and x2 are related to y1 and y2 only and the inverse function becomes:

    f^(-1)(y1,y2) = 1/2*(y1 + y2, y1- y2)

    I think mathematicians like it better is the argument in f() is named x so one renames

    f^(-1)(x1,x2) = 1/2*(x1 + x2, x1 - x2)

    cool
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